Journal of the Indonesian Mathematical Society

The Locating-Chromatic Number of Some Jellyfish Graphs

Arfin Arfin — Fri, 07 Mar 2025 00:00:00 +0000

Let c be a proper coloring of a graph G = (V, E) with k colors which induces a partition Π of V (G) into color classes L1, L2, . . . , Lk . For each vertex v in G, the color code cΠ(v) is defined as the ordered k-tuple (d(v, L1), d(v, L2), . . . , d(v, Lk )), where d(v, Li) represents the minimum distance from v to all other vertices u in Li(1 ≤ i ≤ k). If every vertex possesses unique color codes, then c is called a locating-k-coloring in G. If k is the minimum number such that c is a locating-k-coloring in G, then the locating-chromatic number of G is χL(G) = k. In this paper, the author determine the locating-chromatic number of some Jellyfish Graphs.

On Energy of Prime Ideal Graph of A Commutative Ring Associated with Seidel-Based Matrices

Mamika Ujianita Romdhini — Wed, 05 Mar 2025 00:00:00 +0000

Some energies of the prime ideal graph are found for a commutative ring associated with Seidel-based matrices including Seidel, Seidel Laplacian, and Seidel signless Laplacian matrices.

Forgotten Topological Index of The Zero Divisor Graph for Some Rings of Integers

Ghazali Semil @ Ismail, Nor Haniza Sarmin, Nur Idayu Alimon, Fariz Maulana — Thu, 06 Mar 2025 00:00:00 +0000

A topological index is a numerical value that provides information about the structure of a graph. Among various degree-based topological indices, the forgotten topological index (F-index) is of particular interest in this study. The F-index is calculated for the zero divisor graph of a ring R. In graph theory, the zero divisor graph of R is defined as a graph with vertex set the zero-divisors of R, and for distinct vertices a and b are adjacent if a · b = 0. This research focuses on the zero divisor graph of the commutative ring of integers modulo 2ρn where ρ is an odd prime and n is a positive integer. The objectives are to determine the set of all zero divisors, analyze the vertex degrees of the graph, and then compute the F-index of the zero divisor graph. Using algebraic techniques, we derive the degree of each vertex, the distribution of vertex degrees, and the number of edges in the graph. The general expression for the F-index of the zero divisor graph for the ring is established. The results contribute to understanding topological indices for algebraic structures, with potential applications in chemical graph theory and related disciplines.

Some Topological Indices of Order Divisor Graphs of Cyclic Groups

Agista Surya Bawana, Yeni Susanti — Thu, 06 Mar 2025 00:00:00 +0000

This study investigates order divisor graphs' structural and topological properties derived from cyclic groups. Focusing on the relationship between group order and graph topology, we explore key indices, including the Wiener index, the Harary index, the first Zagreb index, and the second Zagreb index. We use a case-based approach to analyze graphs for cyclic groups of varying orders, from prime powers to more general composite structures. This work extends the theoretical framework of order divisor graphs and provides explicit formulations for their topological indices, highlighting the interplay between algebraic and graph-theoretic properties. These findings contribute to the broader understanding of algebraic graph theory and its applications.

Predicting Stock Price Using Convolutional Neural Network and Long Short Term Memory (Case Study: Stock of BBCA)

Zubaidah Pangestika, Bony Parulian Josaphat — Fri, 07 Mar 2025 00:00:00 +0000

Stocks are capital market instruments capable of creating profits for investors. However, stocks have a fluctuating nature that can lead to risk, so price predictions are needed to reduce this risk. Stock price prediction can use various methods such as deep learning. This study aims to predict stock price using Convolution Neural Network (CNN) and Long Short Term Memory (LSTM), with the application carried out at the stock price of Bank Central Asia (BBCA) for the period between July 1, 2005 and December 30, 2022. Data division uses a ratio of 70% for training and 30% for testing. To maximize prediction results, we select the best hyperparameter combinations using Grid Search. The prediction results show that CNN is better to LSTM, where CNN produces RMSE values of 488.992, R2 83.8%, and MAPE 6.5%.

On Generalized Space Matter Tensor

Bikiran Das, Sanjib Kumar Jana, Sanjoy Kumar Ghosh, Kanak Kanti Baishya — Fri, 07 Mar 2025 00:00:00 +0000

Extending the concept of Petrov tensor, in this article we attempt to introduce generalised space matter tensor [1],[2], [3], [4]. In the Riemannian manifold, it is found that the second Bianchi identity for the generalized space-matter tensor is satisfied if the energy-momentum tensor is of Codazzi type [5]. We study the nature of Riemannian manifolds by imposing curvature restrictions like symmetry, recurrent, weakly symmetry [6], [7], [8] etc. on this generalized Petrov space-matter tensor. We obtain the eigen values of the Ricci tensor S corresponding to the vector fields associated with the various 1− forms.

Double Intervention Analysis on The Arima Model of Covid-19 Cases in Bali

Nurfitri Imro'ah, Nur'ainul Miftahul Huda — Wed, 05 Mar 2025 00:00:00 +0000

The time series process is not only influenced by previous observations, but some phenomena result in drastic changes to observations in the time series process so that there is a change in the average or only a temporary change in observations. For example, there is a policy from the government towards handling a case. This is referred to as an intervention. Therefore, it is necessary to do time series modeling with intervention factors. One form of intervention in the current pandemic era is a policy issued by the government. In this study, the time series model used is ARIMA. This study aimed to analyze the effect of an intervention on the ARIMA model on Covid-19 cases in Bali. This study uses data on the number of new Covid-19 cases in Bali from 24 April 2020 to 31 May 2021. There are two interventions used in this study, namely restrictions on activities for the Panca Yadnya ceremony and crowds in Bali and restrictions on traveling outside the area and/or going home and/or leaving for employees of the State Civil Apparatus during the Covid-19 pandemic. The results of this study show that two policies issued by the Bali provincial government can handle the addition of new cases of Covid-19. It can be seen from the decline in the number of new Covid-19 cases in Bali until the end of May 2021.

Joint-Life Insurance Premium Model Using Archimedean Copula: The Study of Mortality in Indonesia

Fri, 07 Mar 2025 00:00:00 +0000

Joint-life insurance pays a sum insured when the first death occurs. This insurance has a case based on the order of exit from the cohort, namely joint life and last survivor. The former means that one of the insured leaves the cohort, while the latter means the last member of the insured has left his or her cohort. For some reasons of simplicity, the insurance premium is usually calculated with the assumption that the husband and wife are mutually independent. However, this assumption is considered unrealistic. Couples are open to the same risks, hence explaining joint survival model should involve dependence structures between the distribution of spouse mortality. In line with this, to understand the dependence structure of multiple random variables, the approach used is Copula. In this context, Copula relates the marginal distribution function of these variables to the joint life distribution. One of the advantages from Copula is that the random variables do not have to come from the same distribution, hence Copula is considered good enough to explain the dependence of the mortality rate between husband and wife. This study aimed to develop a joint survival model for calculating joint life insurance premiums using the concept of Archimedean Copula to discover the minimum premium value by conducting the following steps: first, identifying the marginal distributions of mortality for genders using Indonesian Mortality Table IV (TMI/
Tabel Mortalitas Indonesia IV); second, Archimedean copula function-based constructing survival models that captures the relationship between these variables; third, setting dependency parameter θ; fourth, calculating the joint life premium using Archimedean copula based survival modeled for each correlation dependency level; and carrying out optimization to find the minimum premium value. This can be achieved by formulating the problem as an optimization problem, considering an objective function that yields the lowest premium till satisfying the financial requirements of the insurance company.